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Nonlinear Constrained Optimization: Methods and Software

ARGONNE NATIONAL LABORATORY9700 South Cass AvenueArgonne, Illinois 60439 Nonlinear Constrained optimization : Methods and SoftwareSven Leyffer and Ashutosh MahajanMathematics and Computer Science DivisionPreprint ANL/MCS-P1729-0310 March 17, 2010 This work was supported by the Office of Advanced Scientific Computing Research, Office of Science, Departmentof Energy, under Contract Background and Introduction12 Convergence Test and Termination Conditions23 Local Model: Improving a Solution Linear and Quadratic Programming .. Methods ..54 Globalization Strategy: Convergence from Remote Starting Lagrangian Methods .. and Merit Function Methods .. and Funnel Methods .. Effect and Loss of Fast Convergence.

A simplified algorithmic framework for solving (1.1) is as follows. Given initial estimate x 0 2IRn, set k= 0; while x kis not optimal do repeat Approximately solve and refine a local model of (1.1) around x k. until an improved solution estimate x k+1 is found ; Check whether x k+1 is optimal; set k= k+ 1. end

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